Cone beam CT projections of an object are a function of scanning trajectory, that is, the relative positions of the irradiating source and the object. Generally, such a trajectory includes rotation about a rotational axis intersecting the object, similar to conventional CT. Of particular interest is imaging of a quasi-short object, which is the reconstruction of a short portion of a long object from longitudinally truncated cone beam data.
In a spherical coordinate system, the two angular coordinates of a trajectory sample, i.e., the angle in the fan direction (Phi—φ) and the cone direction (Theta—θ) can be viewed as a 2D vector in a Phi/Theta plane, and respective ranges of Phi and Theta define the trajectory range.
FIG. 1 illustrates examples of prior art scanning trajectories in terms of (φ, θ) coordinates. A simple CBCT trajectory is circular (indicated by reference numeral 1 in FIG. 1), consisting of a single revolution in the fan angle φ direction about a longitudinal axis of the object. Data sets (projections) associated with such a trajectory are theoretically insufficient for precise object reconstruction. However, approximate reconstructions such as the one suggested by L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm”, JOSA A, Vol. 1, Issue 6, pp. 612-619 (1984), are commonly implemented. Such approximate algorithms may not be adequate for estimating object density values with sufficient precision required for radiotherapy treatment planning. Reconstruction error increases with increased beam cone angle.
Precise reconstruction algorithms require scanning trajectories incorporating sufficiently large Phi/Theta domain. Criteria for adequate CBCT scanning trajectories are described by Bruce D. Smith, “Image Reconstruction From Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods”, IEEE Transactions on Medical Imaging, Volume MI-4, No. 1, pages 14-25 (March 1985). Helical trajectories (indicated by reference numeral 2 in FIG. 1), widely used in conventional CT scanning, are sufficient for precise CBCT reconstruction.
Saddle-curve cone-beam trajectory is described by Pack, J. D., F. Noo, and R Kudo, “Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry”, Phys Med Biol, 2004, 49(11): pp. 2317-36, and by Yu, H. Y., et al., “Exact BPF and FBP algorithms for nonstandard saddle curves”, Medical Physics, 2005, 32(11): pp. 3305-3312). Saddle curves can be directly implemented by rotating an x-ray source on a gantry about a rotational axis while simultaneously driving the source back and forth few times along the rotational axis.
Other trajectories typically related to motion of a single source have been described. For example, U.S. Pat. No. 7,782,999 to Lewalter et al. describes a hybrid system incorporating mechanical source housing rotation about the object and electronic beam steering along the rotational axis. U.S. Pat. No. 5,278,884 to Eberhard et al. describes sinusoidal, square wave (indicated by reference numeral 3 in FIG. 1), circular, and arc trajectories on a sphere. U.S. Pat. No. 7,197,105 to Katsevich describes a scanning trajectory composed of a curve on a plane (e.g., a plane orthogonal to a rotational axis) and of a line perpendicular to the plane. U.S. Pat. No. 6,983,034 to Wang et al. describes substantially circular, helical, spiral, or spiral-like scanning trajectories. U.S. Pat. No. 6,580,777 to Ueki et al. describes rotating the source about an object while simultaneously tilting the rotational axis relative to the object. US Patent Application 2010/0202583 to Wang et al. describes combined rotation of a source about the object and in a plane facing the object.
Trajectory samples form a sampling pattern on the Phi/Theta plane. The pattern density can be defined as the maximal distance between any vector in the trajectory domain and the nearest trajectory sample.
Typical CBCT scanning trajectories (such as the one ones mentioned above) are low density: the associated density is much larger than the space between subsequent samples. Consequently, the associated sampling patterns are uniquely related to the respective trajectories such that reconstruction algorithms designed for a particular trajectory cannot be used for another—the respective sampling patterns are too different.
An example of prior art low-density pattern is seen in FIG. 2, which illustrates a sampling pattern of a low-density triangular wave trajectory.
Characterizing data acquisition geometry only by scanning trajectory assumes adequate detector size and positioning. U.S. Pat. No. 6,041,097 to Roos et al. describes using a flat panel detector for CBCT. Cone beam magnification requires large area detectors for CBCT. Detector width reduction may be achieved by incorporating multiple sources irradiating the object from different angles. For example, U.S. Pat. No. 7,106,825 to Gregerson et al. describes a combination of several smaller detectors. U.S. Pat. No. 7,760,852 to Chen et al. describes a half-width detector combined with a full circular trajectory. U.S. Pat. No. 7,639,775 to DeMan et al. describes offset sources respectively operable to irradiate object radial segments. U.S. Pat. No. 7,062,006 to Pelc et al. describes inverse geometry CT incorporating 2D array of radiation sources configured to respectively emit finely-collimated beams toward a common small detector.